MAYBE

Problem:
 from(X) -> cons(X,from(s(X)))
 length(nil()) -> 0()
 length(cons(X,Y)) -> s(length1(Y))
 length1(X) -> length(X)

Proof:
 DP Processor:
  DPs:
   from#(X) -> from#(s(X))
   length#(cons(X,Y)) -> length1#(Y)
   length1#(X) -> length#(X)
  TRS:
   from(X) -> cons(X,from(s(X)))
   length(nil()) -> 0()
   length(cons(X,Y)) -> s(length1(Y))
   length1(X) -> length(X)
  Usable Rule Processor:
   DPs:
    from#(X) -> from#(s(X))
    length#(cons(X,Y)) -> length1#(Y)
    length1#(X) -> length#(X)
   TRS:
    
   TDG Processor:
    DPs:
     from#(X) -> from#(s(X))
     length#(cons(X,Y)) -> length1#(Y)
     length1#(X) -> length#(X)
    TRS:
     
    graph:
     length1#(X) -> length#(X) ->
     length#(cons(X,Y)) -> length1#(Y)
     length#(cons(X,Y)) -> length1#(Y) -> length1#(X) -> length#(X)
     from#(X) -> from#(s(X)) -> from#(X) -> from#(s(X))
    Restore Modifier:
     DPs:
      from#(X) -> from#(s(X))
      length#(cons(X,Y)) -> length1#(Y)
      length1#(X) -> length#(X)
     TRS:
      from(X) -> cons(X,from(s(X)))
      length(nil()) -> 0()
      length(cons(X,Y)) -> s(length1(Y))
      length1(X) -> length(X)
     SCC Processor:
      #sccs: 2
      #rules: 3
      #arcs: 3/9
      DPs:
       from#(X) -> from#(s(X))
      TRS:
       from(X) -> cons(X,from(s(X)))
       length(nil()) -> 0()
       length(cons(X,Y)) -> s(length1(Y))
       length1(X) -> length(X)
      Open
      
      DPs:
       length1#(X) -> length#(X)
       length#(cons(X,Y)) -> length1#(Y)
      TRS:
       from(X) -> cons(X,from(s(X)))
       length(nil()) -> 0()
       length(cons(X,Y)) -> s(length1(Y))
       length1(X) -> length(X)
      Open